Preheat oven to 350°F (180°C). Spray an 81⁄2x41⁄2- inch loaf pan with baking spray with flour. Line pan with parchment paper, letting excess extend over sides of pan.
In a medium bowl, whisk together flour, salt, baking soda, cinnamon, baking powder, and nutmeg.
In a large bowl, whisk together mashed banana, 3⁄4 cup (165 grams) brown sugar, oil, sour cream, eggs, melted butter, and vanilla. Gently stir flour mixture into banana mixture just until dry ingredients are moistened. Fold in diced banana until no flour streaks remain. Spread batter into prepared pan. Sprinkle remaining 2 tablespoons (28 grams) brown sugar onto batter.
Bake until a wooden pick inserted in center comes out clean, 55 minutes to 1 hour, loosely covering with foil during final 15 minutes of baking to prevent excess browning. Let cool in pan on a wire rack for 10 minutes. Remove from pan, and let cool completely on a wire rack. Store in an airtight container for up to 3 days.